In asymmetrical digital subscriber line (ADSL) systems, Reed-Solomon encoding is used to perform forward error detection and correction. This Reed-Solomon encoding is typically performed by using a linear feedback shift register which must have access to sixteen different sets of unique generator polynomials which must be stored in memory. The total number of coefficients which must be stored in memory in order to provide the sixteen different sets for the Reed-Solomon encoder is one hundred and twenty. In order to provide the one hundred and twenty generator polynomial coefficients, most asymmetrical digital subscriber line (ADSL) systems provide the one hundred and twenty coefficients within read only memory (ROM) memory. This ROM memory consumes a significant amount of substrate surface area which adds costs to the ADSL system. Therefore, a need exists for a Reed-Solomon encoding scheme which does not require a significant amount of ROM memory for coefficient storage while maintaining asymmetrical digital subscriber line (ADSL) operation at frequencies equal to or greater than 55 MHz.